Product form approximations for highly linear loss networks with trunk reservation

Admission controls, such as trunk reservation, are often used in loss networks to optimise their performance. Since the numerical evaluation of performance measures is complex, much attention has been given to finding approximation methods. The Erlang Fixed-Point (EFP) approximation, which is based on an independent blocking assumption, has been used for networks both with and without controls. Several more elaborate approximation methods which account for dependencies in blocking behaviour have been developed for the uncontrolled setting. This paper is an exploratory investigation of extensions and synthesis of these methods to systems with controls, in particular, trunk reservation. In order to isolate the dependency factor, we restrict our attention to a highly linear network. We will compare the performance of the resulting approximations against the benchmark of the EFP approximation extended to the trunk reservation setting. By doing this, we seek to gain insight into the critical factors in constructing an effective approximation. (C) 2003 Elsevier Ltd. All rights reserved.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Using the flexibility index to compare batch and continuous activated sludge processes

This paper considers the question of which is better: the batch or the continuous activated sludge processes? It is an important question because dissension still exists in the wastewater industry as to the relative merits of each of the processes. A review of perceived differences in the processes from the point of view of two related disciplines, process engineering and biotechnology, is presented together with the results of previous comparative studies. These reviews highlight possible areas where more understanding is required. This is provided in the paper by application of the flexibility index to two case studies. The flexibility index is a useful process design tool that measures the ability of the process to cope with long term changes in operation.

The Lake Tekapo experiment (LTEX): An investigation of atmospheric boundary layer processes in complex terrain

A research program on atmospheric boundary layer processes and local wind regimes in complex terrain was conducted in the vicinity of Lake Tekapo in the southern Alps of New Zealand, during two 1-month field campaigns in 1997 and 1999. The effects of the interaction of thermal and dynamic forcing were of specific interest, with a particular focus on the interaction of thermal forcing of differing scales. The rationale and objectives of the field and modeling program are described, along with the methodology used to achieve them. Specific research aims include improved knowledge of the role of surface forcing associated with varying energy balances across heterogeneous terrain, thermal influences on boundary layer and local wind development, and dynamic influences of the terrain through channeling effects. Data were collected using a network of surface meteorological and energy balance stations, radiosonde and pilot balloon soundings, tethered balloon and kite-based systems, sodar, and an instrumented light aircraft. These data are being used to investigate the energetics of surface heat fluxes, the effects of localized heating/cooling and advective processes on atmospheric boundary layer development, and dynamic channeling. A complementary program of numerical modeling includes application of the Regional Atmospheric Modeling System (RAMS) to case studies characterizing typical boundary layer structures and airflow patterns observed around Lake Tekapo. Some initial results derived from the special observation periods are used to illustrate progress made to date. In spite of the difficulties involved in obtaining good data and undertaking modeling experiments in such complex terrain, initial results show that surface thermal heterogeneity has a significant influence on local atmospheric structure and wind fields in the vicinity of the lake. This influence occurs particularly in the morning. However, dynamic channeling effects and the larger-scale thermal effect of the mountain region frequently override these more local features later in the day.

Online titrimetric and off-gas analysis for examining nitrification processes in wastewater treatment

The two steps of nitrification, namely the oxidation of ammonia to nitrite and nitrite to nitrate, often need to be considered separately in process studies. For a detailed examination, it is desirable to monitor the two-step sequence using online measurements. In this paper, the use of online titrimetric and off-gas analysis (TOGA) methods for the examination of the process is presented. Using the known reaction stoichiometry, combination of the measured signals (rates of hydrogen ion production, oxygen uptake and carbon dioxide transfer) allows the determination of the three key process rates, namely the ammonia consumption rate, the nitrite accumulation rate and the nitrate production rate. Individual reaction rates determined with the TOGA sensor under a number of operation conditions are presented. The rates calculated directly from the measured signals are compared with those obtained from offline liquid sample analysis. Statistical analysis confirms that the results from the two approaches match well. This result could not have been guaranteed using alternative online methods. As a case study, the influences of pH and dissolved oxygen (DO) on nitrite accumulation are tested using the proposed method. It is shown that nitrite accumulation decreased with increasing DO and pH. Possible reasons for these observations are discussed. (C) 2003 Elsevier Science Ltd. All rights reserved.

In situ characterization of stickiness of sugar-rich foods using a linear actuator driven stickiness testing device

A stickiness testing device based on the probe tack test has been designed and tested. It was used to perform in situ characterization of drying hemispherical drops with an initial radius 3.5 mm. Tests were carried out in two drying temperatures, 63 and 95 degreesC. Moisture and temperature histories of the drying drops of fructose, honey, sucrose, maltodextrin and sucrose-maltodextrin mixtures were determined. The rates of moisture evaporation of the fructose solution was the fastest while those of the maltodextrin solution was the lowest. A profile reversal was observed when the temperature profiles of these materials were compared. Different modes of failure were observed during the stickiness tests. Pure fructose and honey solutions remained completely sticky and failed cohesively until the end of drying. Pure sucrose solution remained sticky and failed cohesively until complete crystallization occurred. The surface of the maltodextrin drops formed a skin shortly after the start of drying. It exhibited adhesive failure and reached a state of non-adhesion. Addition of maltodextrin significantly altered the stickiness of sucrose solution. (C) 2002 Elsevier Science Ltd. All rights reserved.

A class B switch-mode assisted linear amplifier

A switch-mode assisted linear amplifier (SMALA) combining a linear (Class B) and a switch-mode (Class D) amplifier is presented. The usual single hysteretic controlled half-bridge current dumping stage is replaced by two parallel buck converter stages, in a parallel voltage controlled topology. These operate independently: one buck converter sources current to assist the upper Class B output device, and a complementary converter sinks current to assist the lower device. This topology lends itself to a novel control approach of a dead-band at low power levels where neither class D amplifier assists, allowing the class B amplifier to supply the load without interference, ensuring high fidelity. A 20 W implementation demonstrates 85% efficiency, with distortion below 0.08% measured across the full audio bandwidth at 15 W. The class D amplifier begins assisting at 2 W, and below this value, the distortion was below 0.03%. Complete circuitry is given, showing the simplicity of the additional class D amplifier and its corresponding control circuitry.

A new wavelet-based adaptive method for solving population balance equations

A new wavelet-based adaptive framework for solving population balance equations (PBEs) is proposed in this work. The technique is general, powerful and efficient without the need for prior assumptions about the characteristics of the processes. Because there are steeply varying number densities across a size range, a new strategy is developed to select the optimal order of resolution and the collocation points based on an interpolating wavelet transform (IWT). The proposed technique has been tested for size-independent agglomeration, agglomeration with a linear summation kernel and agglomeration with a nonlinear kernel. In all cases, the predicted and analytical particle size distributions (PSDs) are in excellent agreement. Further work on the solution of the general population balance equations with nucleation, growth and agglomeration and the solution of steady-state population balance equations will be presented in this framework. (C) 2002 Elsevier Science B.V. All rights reserved.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.